Improved-Efficacy Optimization of Compact Microwave Passives by Means of Frequency-Related Regularization

Electromagnetic (EM)-driven optimization is an important part of microwave design, especially for miniaturized components where the cross-coupling effects in tightly arranged layouts make traditional (e.g., equivalent network) representations grossly inaccurate. Efficient parameter tuning requires reasonably good initial designs, which are difficult to be rendered for newly developed structures or when re-design for different operating conditions or material parameters is required. If global search is needed, due to either the aforementioned issues or multi-modality of the objective function, the computational cost of the EM-driven design increases tremendously. This paper introduces a frequency-related regularization as a way of improving the efficacy of simulation-based design processes. Regularization is realized by enhancing the conventional (e.g., minimax) objective function using a dedicated penalty term that fosters the alignment of the circuit characteristics (e.g., the operating frequency or bandwidth) with the target values specified by the design requirement. This leads to smoothening of the objective function landscape, improves reliability of the optimization process, and reduces its computational cost as compared to the standard formulation. An added benefit is the increased immunity to poor initial designs and multi-modality issues. In particular, regularization can make local search routines sufficient in situations where global optimization would normally be necessary. The presented approach is validated using two miniaturized circuits, a rat-race and a branch line coupler. The numerical results demonstrate its superiority over conventional design problem formulations in terms of reliability of the optimization process.